Problem: Solve for $x$ : $2\sqrt{x} + 10 = 9\sqrt{x} + 6$
Explanation: Subtract $2\sqrt{x}$ from both sides: $(2\sqrt{x} + 10) - 2\sqrt{x} = (9\sqrt{x} + 6) - 2\sqrt{x}$ $10 = 7\sqrt{x} + 6$ Subtract $6$ from both sides: $10 - 6 = (7\sqrt{x} + 6) - 6$ $4 = 7\sqrt{x}$ Divide both sides by $7$ $\frac{4}{7} = \frac{7\sqrt{x}}{7}$ Simplify. $\dfrac{4}{7} = \sqrt{x}$ Square both sides. $\dfrac{4}{7} \cdot \dfrac{4}{7} = \sqrt{x} \cdot \sqrt{x}$ $x = \dfrac{16}{49}$